A General Theory of Classificatory Sorting Strategies: 1. Hierarchical Systems

Lance, G. N.; Williams, W. T.

doi:10.1093/comjnl/9.4.373

Cited by 1,443 publications

(630 citation statements)

References 15 publications

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“…An interesting updating scheme for dissimilarities in agglomerative hierarchical clustering has been proposed in [87] and extended in [79,80]. A parametric formula gives new dissimilarity values between cluster C k and C i , C j when these last two are merged:…”

Section: Agglomerative Hierarchical Clustering Algorithmsmentioning

confidence: 99%

Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

411

251

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Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds F.C.A.R. Cluster Analysis and Mathematical ProgrammingPierre Hansen GERAD andÉcole des HautesÉtudes Commerciales Montréal, CanadaBrigitte Jaumard GERAD andÉcole Polytechnique de Montréal Canada February, 1997Les Cahiers du GERAD G-97-10Abstract Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are homogeneous and/or well separated. As many types of clustering and criteria for homogeneity or separation are of interest, this is a vast field. A survey is given from a mathematical programming viewpoint.Steps of a clustering study, types of clustering and criteria are discussed. Then algorithms for hierarchical, partitioning, sequential, and additive clustering are studied. Emphasis is on solution methods, i.e., dynamic programming, graph theoretical algorithms, branch-and-bound, cutting planes, column generation and heuristics.

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Section: Agglomerative Hierarchical Clustering Algorithmsmentioning

confidence: 99%

Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

411

251

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“…Assuming that significant levels of individual diet specialization were detected at each site, we used Hierarchical Cluster Analysis to classify otters into groups of animals having similar diet specializations, following previously-published methods (Tinker 2004. For this analysis we treated individual sea otters from both sites as experimental units, key prey types (those prey types comprising over 5% of diets overall) as variables, Euclidean distances were used as diet similarity measures, and clusters were identified using the Lance-Williams "flex beta" clustering algorithm with beta = -.25 (Lance andWilliams 1967, Scheibler andSchneider 1985). We selected the optimal number of clusters based on profile plots of Root mean square standard deviation (RMSSTD) and the pseudo-F value (the optimal number of clusters is expected to produce a local minima of the RMSSTD and a maximal value of the pseudo-F value).…”

Section: Methodsmentioning

confidence: 99%

The High Cost of Motherhood: End-Lactation Syndrome in Southern Sea Otters (Enhydra Lutris Nereis) on the Central California Coast, Usa

Chinn

Miller

Tinker

et al. 2016

Journal of Wildlife Diseases

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“…They generate a classification in a bottom-up manner, by a series of agglomerations in which small clusters, initially containing individual molecules, are fused together to form progressively larger clusters, with the most similar pair of clusters being fused at each stage of the classification. The various hierarchic agglomerative methods differ only in the criterion that is used to select the most similar pair of clusters at each stage; indeed, they can all be implemented using a common algorithm first described in detail by Lance and Williams [20] (although more efficient algorithms are available for individual clustering methods [21]). …”

Section: The Székely-rizzo Clustering Methodsmentioning

confidence: 99%

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

Varin

Bureau

Mueller

et al. 2009

Journal of Molecular Graphics and Modelling

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Ward's method is extensively used for clustering chemical structures represented by 2D fingerprints. This paper compares Ward clusterings of 14 datasets (containing between 278 and 4332 molecules) with those obtained using the Székely-Rizzo clustering method, a generalization of Ward's method. The clusters resulting from these two methods were evaluated by the extent to which the various classifications were able to group active molecules together, using a novel criterion of clustering effectiveness. Analysis of a total of 1400 classifications (Ward and Székely-Rizzo clustering methods, fourteen different datasets, five different fingerprints and ten different distance coefficients) demonstrated the general superiority of the Székely-Rizzo method. The distance coefficient first described by Soergel performed extremely well in these experiments, and this was also the case when it was used in simulated virtual screening experiments.

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A General Theory of Classificatory Sorting Strategies: 1. Hierarchical Systems

Cited by 1,443 publications

References 15 publications

Cluster analysis and mathematical programming

Cluster analysis and mathematical programming

The High Cost of Motherhood: End-Lactation Syndrome in Southern Sea Otters (Enhydra Lutris Nereis) on the Central California Coast, Usa

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

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